DRP

Bergman. An Invitation to General Algebra and Universal Constructions

Speyer, David, and Sturmfels, Bernd. Tropical Mathematics
Richter-Gebert, Sturmfels, and Theobald. First Steps in Tropical Geometry

Cox, Little, and O'Shea. Ideals, Varieties, and Algorithms.

Dummit and Foote. Abstract Algebra, 3rd Edition.
Eisenbud. Commutative Algebra

Cox, Little, and O'Shea. Ideals, Varieties, and Algorithms
?. Modern Computer Algebra

Kirwan, Francis. (?)

Smith. An invitation to Algebraic Geometry

Fulton, William. Algebraic Curves

Professor Ngo's course on automorphic forms.

Tate and Silverman. Rational Points on Elliptic Curves
Koblitz. A Course in Number Theory and Cryptography

Milne. Notes on algebraic number theory.

Borevich and Shafarevich. Number Theory
Marcus, Daniel. Number Fields

Koblitz. A Course in Cryptography and Number Theory

Silverman. Elliptic Curves

Tate and Silverman. Rational Points on Elliptic Curves

Iwasawa, Kenkichi. Local class field theory. Oxford Science Publications, 1986
Yoshida, Teruyoshi. Local class field theory via Lubin-Tate theory. Ann. Fac. Sci. Toulouse Math. (6) 17 (2008), no. 2, 411--438.

Matousek, Jiri. Using the Borsuk-Ulam Theorem

Bott and Tu. Differential Forms in Algebraic Topology.

The Knot Book
Munkres. Topology

Bott and Tu. Differential Forms in Algebraic Topology

Aguilar et al. Algebraic Topology from a Homotopical Viewpoint.
May, J.P. A Concise Course in Algebraic Topology

Jones, Frank. Lebesgue Integration on Euclidean Space

Apostol. Analytic Number Theory

Serre. A Course in Arithmetic

Maclane. Categories for the Working Mathematician

Goldblatt. Topoi: The categorial analysis of logic
Borceaux. Handbook of categorical algebra I
MacLane, Moerdijk. Sheaves in Geometry and Logic
Awodey. Category Theory
McClarty. Elementary Category Theory

Awodey. Category Theory
Maclane. Categories for the Working Mathematician.
May. A Concise Course in Algebraic Topology

Awodey. Category Theory

Awodey. Category Theory

Lambek and Scott
Awodey. Category Theory

May. A Concise Course in Algebraic Topology II
Dwyer and Spalinski. Homotopy Theory and Model Categories

Awodey. Category Theory

Conway. On Numbers and Games

Conway. On Numbers and Games
Berlekamp, Massey, Guy. Winning Ways For Your Mathematical Plays

Conway. On Numbers and Games

Conway. On Numbers and Games.
Berlekamp, Conway, and Guy. Winning Ways For Your Mathematical Plays

Conway. On Numbers and Games
Berlekamp, Conway, and Guy. Winning Ways For Your Mathematical Plays

Erdos and Suranyi. Topics in Number Theory

Apostol. Analytic number theory

Stein and Shakarchi. Complex Analysis

Needham, Tristan. Visual Complex Analysis. Oxford University Press

http://www.cs.princeton.edu/theory/index.php/Compbook/Draft
Kearns and Vazirani. An Introduction to Computational Learning Theory

Gamelin and Greene. Introduction to Topology

Strauss, Walter A. Partial Differential Equations: An Introduction

Do Carmo. Differential Geometry of Curves and Surfaces

Janich, Klaus. Vector Analysis
Lee, John. Introduction to Smooth Manifolds

Milnor
Guillemin and Pollack. Differential Topology

Guillemin and Pollack. Differential Topology

do Carmo. Differential Geometry of Curves and Surfaces
do Carmo. Riemannian Geometry

Hamilton's papers on the Ricci flow.

do Carmo. Differential forms and applications
Bachman, David. A Geometric Approach to Differential Forms
Morita, Shigeyuchi. Geometry of Differential Forms

Bott and Tu. Differential Forms in Algebraic Topology.
Milnor and Stasheff. Characteristic Classes.
Hatcher. Vector Bundles and K-Theory

Thurston. three-dimensional geometry and topology.

Guillemin and Pollack. Differential topology
Milnor. Morse theory
Milnor. Topology from the Differentiable Viewpoint

Schutz, Bernard. A First Course in General Relativity
Kühnel, Wolfgang. Differential Geometry: Curves - Surfaces - Manifolds

Laczkovich, Miklos. Conjecture and Proof

Jones and Jones. Elementary Number Theory

Silverman, Joseph. A Friendly Introduction to Number Theory

Jones and Jones. Elementary Number Theory

Pollicott. (book on dynamical systems of ergodic theory)

Einsiedler and Ward. Ergodic theory with a view towards number theory

Korner. Fourier Analysis

Stein. Fourier Analysis

Stein. Fourier Analysis

Stein. Fourier Analysis

Stein. Fourier Analysis

Duoandikoetxea, Javier. Fourier Analysis

Vretblad, Anders. Fourier analysis and its applications

Terras. Fourier Analysis on Finite Groups and Applications
Stein. Fourier Analysis: An Introduction

Falconer. Fractal Geometry

Hassani, S. Mathematical Physics
Reed and Simon. Methods of Modern Mathematical Physics

Serre. Trees
Scot and Wall. Topological Methods in Group Theory.
Farb. Notes from Geometric Literacy.

Biggs, N. Algebraic Graph Theory
Godsil and Royle. Algebraic Graph Theory.

Roberts and Tesman. Applied Combinatorics
Anderson, Ian. Combinatorial Designs: Construction Methods
Tucker, Alan. Applied Combinatorics

Holt, Dereck. Handbook of Computational Group Theory

Stein. Singular Integrals

Stein. Harmonic Analysis

Weibel. An Introduction to Homological Algebra
Gelfand and Manin. Methods of Homological Algebra

Anderson. Hyperbolic Geometry

Iversen, Birger. Hyperbolic Geometry. Anderson, James W. Hyperbolic Geometry

Stillwell. Geometry of Surfaces
Bonahon. Low-dimensional geometry: from euclidean surfaces to hyperbolic knots
Anderson. Hyperbolic Geometry

Morton L. Curtis, Matrix Groups

Hassani, Sadri. Mathematical Physics: A Modern Introduction to Its Foundations

Lee, John M. Introduction to Smooth Manifolds

Baker. Matrix groups, an introduction to Lie groups
Simon. Representations of Finite and Compact groups

Lee, John C. Introduction to smooth manifolds

Axler. Linear Algebra Done Right.
Artin. Algebra

Axler, Sheldon. Linear Algebra Done Right

Mileti, Joseph R. Mathematical Logic for Mathematicians. Course notes, 2007

standard reference by Ebinghaus for Lindstrom's theorem

Marker, David. Model Theory: An Introduction. Springer-Verlag, New York, 2002.
Mileti, Joseph R. Mathematical Logic for Mathematicians. Course notes, 2007

Simpson, Stephen. Subsystems of Second Order Arithmetic

Robbin. Mathematical Logic: A First Course

Jech. Set Theory

Chagrov and Zakharyachev. Modal Logic

Chang, C. C. and Keisler, H. Jerome. Model Theory
Marker, David. Model Theory

Enderton.

Jech. Set theory

Enderton.

Hassani, Sadri. Mathematical Physics

May, Peter. A Concise Course in Algebraic Topology.
Dwyer and Spalinski. Homotopy Theories and Model Categories

Goldblatt. Lectures on the Hyperreals.
Henle and Kleinberg. Infinitesimal Calculus

Sundaram, Rangarajan K. A First Course in Optimization Theory

Lawler, Gregory. Introduction to Stochastic Processes

Williams. Probability with Martingales.

Williams, David. Probability with Martingales.
Cohn, Donald. Measure Theory

Williams, David. Probability with Martingales
Rudin, Walter. Real and Complex Analysis

Ross, Sheldon. Stochastic Processes

Linearity, Symmetry, and Prediction in the Hydrogen Atom. Springer UTM

Fulton. Young Tableaux: With Applications to Representation Theory and Geometry
Fulton and Harris. Representation Theory: A First Course

Kerov.

Fulton and Harris. Representation Theory: A first course

Humphreys, James. Representations of Semisimple Lie Algebras in the BGG Category O

Kirwin. Complex Algebraic Curves
Miranda. Algebraic Curves and Riemann Surfaces.
Farkas and Kra. Riemann Surfaces.

Miranda. Algebraic curves and Riemann surfaces.

Miranda. Algebraic Curves and Riemann Surfaces
Lecture notes from Schlag's first-year graduate complex analysis course.

Miranda. Algebraic Curves and Riemann Surfaces

Jech. Set Theory

Shreve, Steven. Stochastic Calculus for Finance: Continuous-Time Models.
Oksendal, Bernt. Stochastic Differential Equations: An Introduction with Applications

Hochman. Genericity in topological dynamics. (paper)

Maclane and Moerdijk. Sheaves in Geometry and Logic